Theorem zleasym | index | src |

theorem zleasym (a b: nat): $ a <=Z b -> b <=Z a -> a = b $;
StepHypRefExpression
1 zleasymb
a = b <-> a <=Z b /\ b <=Z a
2 1 bi2i
a <=Z b /\ b <=Z a -> a = b
3 2 exp
a <=Z b -> b <=Z a -> a = b

Axiom use

axs_prop_calc (ax_1, ax_2, ax_3, ax_mp, itru), axs_pred_calc (ax_gen, ax_4, ax_5, ax_6, ax_7, ax_10, ax_11, ax_12), axs_set (elab, ax_8), axs_the (theid, the0), axs_peano (peano1, peano2, peano5, addeq, muleq, add0, addS, mul0, mulS)